Spectral Graph Analysis: A Unified Explanation and Modern Perspectives
Subhadeep Mukhopadhyay, Kaijun Wang

TL;DR
This paper seeks to unify spectral graph analysis under a single statistical framework, enhancing understanding and practical algorithm design for complex networks across various fields.
Contribution
It introduces a universal statistical logic that explains and encompasses nearly all spectral graph methods within one formalism.
Findings
Proposes a simple, universal spectral graph analysis framework
Reveals underlying statistical principles of spectral methods
Facilitates improved algorithm development for network analysis
Abstract
Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful techniques and models for understanding `patterns of interconnectedness' in a graph. Our prime focus in this paper is on the following question: Is there a unified explanation and description of the fundamental spectral graph methods? There are at least two reasons to be interested in this question. Firstly, to gain a much deeper and refined understanding of the basic foundational principles, and secondly, to derive rich consequences with practical significance for algorithm design. However, despite half a century of research, this question remains one of the most formidable open issues, if not the core problem in modern network science. The achievement…
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Taxonomy
TopicsComplex Network Analysis Techniques · Topological and Geometric Data Analysis · Bioinformatics and Genomic Networks
